Simple Green is a good mild cleaner that is friendly to wood. The only reason I don't use it is , I just don;t like the smell.
I know some that like to use Purpule Power. It's a good cleaner, but it's strong and can damage the surface if left on to long.
You must be careful that you don't use anything that will cause the natural glues in the wood, that hold the fibers together, to break down.
And like Stonecutter2 said, be conservative.
Different types of wood react differently when it comes to cosmoline and oils. Wood like Elm and Chue wood love to soak up oil and don't let it go as fast as other woods. Beech is not as bad.
Walnut is one of the easiest to clean. It will soak up oil but will let it seep out easily with a little heat.
Birch doesn't soak up much oil and is fairly easy to clean.
Years ago I cleaned up a cosmoline soaked Yugo Mauser stock. It was so soaked that the stock was orange. after cleaning there were a light of light colors streaks in the stock. This is common with Elm. I was told by a bunch of collectors that I had destroyed the stock. I tried to explain that the stock color would even out in a month or two, but they just kept telling that I didn't know what I was talking about.
About a year later I posted new pics of the same gun on the same forum. The same people that had told me that I had destroyed the stock where now saying how nice the stock looked . I just love people that think they know a lot about things they know so little about.